Non-cooperative game theoretic approaches to bilateral exchange networks.

Bilateral exchange networks are structures in which a finite set of players have a restricted framework of bargaining opportunities with each other. The key restrictions are that each player may participate in only one 'exchange' and each of these may only involve a pair of players. There is a large sociology literature which investigates these networks as a simplified model of social exchange. This literature contains many predictions and experimental results, but not a non-cooperative game theoretic analysis. The aim of the thesis is to provide this. The analysis builds on the economic theory literature on non-cooperative bar gaining, principally the alternating offers and Nash demand games. Two novel perfect information models based on the alternating offers game are considered and it is demonstrated that they suffer from several difficulties. In particular, analysis of an example network shows that for these two models multiple subgame perfect equilibria exist with considerable qualitative differences. It is argued that an alternating offers approach to the problem is therefore unlikely to be successful for general networks. Models based on Nash demand games also have multiple solutions, but their simpler structure allows investigation of equilibrium selection by evolutionary methods. An agent based evolutionary model is proposed. The results of computer simulations based on this model under a variety of learning rules are presented. For small networks the agents often converge to unique long-term outcomes which offer support both for theoretical predictions of 2 and 3 player alternating offers models and experimental results of the sociology literature. For larger networks the results become less precise and it is shown they sometimes leave the core. It is argued that a modified evolutionary model has scope for avoiding these difficulties and providing a constructive approach to the problem for large networks

Distilling importance sampling

The two main approaches to Bayesian inference are sampling and optimisation methods. However many complicated posteriors are difficult to approximate by either. Therefore we propose a novel approach combining features of both. We use a flexible parameterised family of densities, such as a normalising flow. Given a density from this family approximating the posterior, we use importance sampling to produce a weighted sample from a more accurate posterior approximation. This sample is then used in optimisation to update the parameters of the approximate density, which we view as distilling the importance sampling results. We iterate these steps and gradually improve the quality of the posterior approximation. We illustrate our method in two challenging examples: a queueing model and a stochastic differential equation model.Comment: This version adds a second application, and fixes some minor error